laqgb(3)

NAME
laqgb - laqgb: row/col scale matrix

SYNOPSIS

  Functions
subroutine claqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
subroutine dlaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
subroutine slaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
subroutine zlaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Detailed Description

Function Documentation

  subroutine claqgb (integer m, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> CLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is REAL
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is REAL
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 158 of file claqgb.f.

  subroutine dlaqgb (integer m, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, character equed)

DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> DLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is DOUBLE PRECISION
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 157 of file dlaqgb.f.

  subroutine slaqgb (integer m, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> SLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is REAL array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is REAL
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is REAL
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 157 of file slaqgb.f.

  subroutine zlaqgb (integer m, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, character equed)

ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> ZLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX*16 array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is DOUBLE PRECISION
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 158 of file zlaqgb.f.

Author

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